How are fractals used by scientists and mathemeticians in the real world today?

Fractals describe geometrical objects that have more and more sub-structure as one views them at higher and higher magnifications.

"Fractals also approximately describe many real-world objects, such as clouds, mountains, turbulence, coastlines, roots and branches of trees and veins and lungs of animals."

Scientists and engineers and mathematicians and other people interested in these objects (such as a computer graphics person working to create an image of an artificial landscape) might use fractals in their work. For example, a biomedical engineer might want to calculate how much surface area covers the bronchial tubes within a human lung. Or maybe an environmentalist wants to estimate how many miles of coastline could be affected by a large oil spill. These are ways that scientists use fractals to describe or approximate the *structure* of a real (or imagined) object.

Another way scientists and mathematicians sometimes use fractals is in the field of nonlinear dynamics, where the behavior of a system is *described* by a geometrical object in something called "phase space." This object can assume many different forms, such as points or loops (circles, polygons, squashed ellipses, etc.). Points indicate the situation when there is no change in behavior, while loops describe when a system does the same thing over and over again continuously, (i.e. it "oscillates"). An example of another shape is a spiral. Dynamicists use the spiral to describe how a pendulum swings back and forth and gradually spirals into the origin as time goes on.

As for fractals, there are some behaviors (often called "chaotic") that are so complex that the geometric object is a fractal, rather than a simpler shape. A cardiologist might monitor a patient's heartbeat and chart its behavior over time. A healthy patient might have a slightly irregular heartbeat, and this might be visible in the record as a fractal. But if the heartbeat becomes too regular, the fractal might morph into a simpler shape, such as a loop, indicating that the patient might be at risk for a heart attack. In this example the fractal is used to help the physician monitor the status of her patient.